We show that the assembly of the solar system terrestrial planets can be successfully modeled with all of the mass initially confined to a narrow annulus between 0.7 and 1.0 AU. With this configuration, analogs of Mercury and Mars often form from the collisional evolution of material diffusing out of the annulus under the scattering of the forming Earth and Venus analogs. The final systems also possess eccentricities and inclinations that match the observations, without recourse to dynamical friction from remnant small body populations. Finally, the characteristic assembly timescale for Earth analogs is rapid in this model and consistent with cosmochemical models based on the 182Hf-182W isotopes. The agreement between this model and the observations suggests that terrestrial planet systems may also be formed in 'planet traps,' as has been proposed recently for the cores of giant planets in our solar system and others.